Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

If a muon is traveling at 70% the speed of light, how long will it take to decay in the observer's rest frame (i. E. , what is the observed lifetime)?.

Sagot :

wiyonopaolina

A muon takes to decay in the observer's rest frame is 3.08 μs.

A muon is an unstable subatomic particle that decays into other particles with a mean lifetime of 2.20 μs. This is in the muon reference frame.

The formula for the relativistic factor

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{v}{c})^2}}[/tex]

  • v = muon's speed = 70% c = 0.7c
  • c = the speed of light
  • γ = the relativistic factor

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{0.7c}{c})^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.49}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{0.51}}[/tex]

[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]

[tex]\gamma \:=\: \frac{1}{0.714}[/tex]

γ = 1.4

Relativistic time interval formula

t = γ t₀

  • t₀ = the time according muon reference frame = 2.20 μs
  • t = the time according to the observer's rest frame

t = 1.4 × 2.2

t = 3.08 μs

Learn more about Relativistic time here: https://brainly.com/question/14857317

#SPJ4

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.